The maximum consensus problem is fundamentally important to robust geometric fitting in computer vision. Solving the problem exactly is computationally demanding, and the effort required increases rapidly with the problem size. Although randomized algorithms are much more efficient, the optimality of the solution is not guaranteed. Towards the goal of solving maximum consensus exactly, we present guaranteed outlier removal as a technique to reduce the runtime of exact algorithms. Specifically, before conducting global optimization, we attempt to remove data that are provably true outliers, i.e., those that do not exist in the maximum consensus set. We propose an algorithm based on mixed integer linear programming to perform the removal. The result of our algorithm is a smaller data instance that admits a much faster solution by subsequent exact algorithms, while yielding the same globally optimal result as the original problem. We demonstrate that overall speedups of up to 80% can be achieved on common vision problems1.